Can using Rank Reporter hurt my website’s ranking?

Answer: No, you cannot affect your website’s ranking by using Rank Reporter. There are two main reasons why this is true:

It is not possible for a search engine to determine which website you are tracking in the search result pages. Rank Reporter only sends your query text to the search engine; it does not send any information about which websites are being tracked.

If it were possible to negatively affect your website’s ranking, then it would also be possible to negatively affect the ranking of your competitors’ sites. This is related to point 1: there is no way for the search engines to determine which website you own, so no site can be penalized in any way.